The world is governed by laws. I don’t mean the human laws, the social consensus or social contract or whatever you want to call it, but the much more rigid laws of nature. They’re everywhere. They are mandatory and they rule over all aspects of our life. Let’s recap a few of them:
The laws of thermodynamics are the most famous. Because of them we are bound to grow old and die, we have to work and we can’t go back in time. Nothing fun here, right?
Physics is full of laws. What about relativity? It may have a better reputation than thermodynamics, but it’s also a harsh mistress. It doesn’t allow us to travel faster than the speed of light; though it might not seem like a big deal, it confines us to remain isolated: we won’t be able to watch a live sports event from another galaxy ever, let alone congratulate the winners.
Then we have the “regular” laws of physics: universal gravitation, the three laws of motion, electromagnetism… They speak of a well-ordered universe, a billiard pool where, if you know the initial position of the balls and the strength and the angle of the first hit, you can predict everything that will happen forever. The only thing you need is a sufficiently large white board. These laws seem innocent, but they’re denying something very special: they are denying our free will.
But don’t worry: it didn’t take. These laws tell us how the macroscopic world works, or maybe we should say how it worked. After everything was discovered and science was over, a discrete revolution by the name of quantum mechanics came along and, though it seems to have preserved our free will, it certainly has thrown away a little thing we used to be very fond of: our common sense.
But enough about physics: the rest of sciences are also choke-full of laws. We have a lot of them in, for example, economics: the law of diminishing returns, supply and demand, the iron law of wages (you don’t know what’s this? Go and read about it and become utterly depressed. It says that real wages always tend toward the minimum wage necessary to sustain the life of the worker). Many of them describe in very creative ways how this world is not the way we’d Iike it to be; they smell of the second law of thermodynamics and maybe they are the second law in disguise.
Even when they’re made-up laws, they have a profound impact on the way we think. The Three Laws of Robotics, as stated by Asimov, prevent an artificial intelligence from killing all the humans, giving birth to a radically different new world.
But none of these laws would be possible without the Great Ruler of All (please play a fanfare on your speakers): Mathematics. I don’t know if there is such thing as the Truth, the immutable and eternal Truth, the capitalised Truth, but I’m fairly sure that math is as close to that Truth as we’re ever gonna get. Yes, God could have chosen any profession in the world, including Hollywood actor(*), but he chose to be a mathematician. Indeed God’s ways are not our ways.
Mathematics is also full of laws, but here they’re called theorems, axioms and corollaries. Make no mistake: they are as ruthless as the rest of them and will make your life equally miserable. And there’s no known way to avoid them. If you pick any number, let’s say your age, multiply it by 3, then add 6, divide it by 3 and subtract the original number, you’ll get the number 2. Always. The initial number doesn’t matter. It doesn’t matter even if it is a natural number or a real number; try it with √3, for example. This happens because math has laws and those laws, until now, have proven to be very reliable.
So let’s recap: we have to grow old and die, we don’t have free will, common sense is good for nothing, no vacation on other galaxies, no money to spend on such vacation, there’s no time travel and no artificial intelligence will ever be a serial killer (these last two dedicated to Terminator). What can we do for fun?
The answer is simple: let’s break the laws. But then the Supreme Ruler (Math) comes and says: “How dare you defy my rules, insect? Don’t you know I taught God how to build the world? Two plus two will always equal four!”
If you go and check, two plus two still equals four, no matter how much you’ve previously rebelled.
But there’s always a caveat. Laws can be ironclad, but they must be applied on realms and therein lies a weakness. Realms show some interesting properties: they have borders, they share their borders with other realms and sometimes this sharing leads to disagreement. And here is where the action is. This is the land of paradoxes, a land full of unexpected consequences and mind-blowing realizations. This is the ground where science and knowledge are pushed forward, beyond their previous inescapable limits. This is the land where the most important mathematical equation rules:
law bending = mind blowing
We’re dedicating this blog to the exploration of those lands. Have fun!